In a comment I've referred you to a question which answers this already. In short, if there's an indirect complement expressed as a full pronoun (in this case [a] ustedes), then the equivalent clitic (short, unstressed) form of the pronoun must appear (les). The same, using other persons and numbers:
- Ella me cocina a mí.
- Ella te cocina a ti.
- Ella le cocina a él.
- Ella nos cocina a nosotros.
- Ella les cocina a ellos.
(This is just a grammar rule, i. e. just how the language works.)
As to why ustedes would be used if les is already in use: for emphasis. You can very well do without it (Ella les cocina). Adding it explicitly simply emphasizes the fact that someone is cooking for you, not incidentally but purposefully, not someone else but you. In this example it could also be useful to avoid ambiguity because les on its own can mean "you" (plural) or "them" (except in Spain, where plural "you" is vosotros).
Some time ago we discussed (but I can't find that question) the equivalence between these and phrases with para:
Ella les cocina a ustedes. ~= Ella cocina para ustedes.
As you see there's no need to use the clitic pronoun in the equivalent phrase.